Fire director apparatus for antiaircraft guns



Oct. 2, 1945. A. svoBoDA 2,385,952

FIRE DIRECTOR APPARATUS FOR ANTIAIRCRAFT GUNS Filed May 23, 1941 ll Sheets-Sheet l Fwwax-vemsw INVEN OR. 5% /01 Oct. 2, 194-5.

A.SVOBODA FIRE DIRECTOR APPARATUS FOR ANTIAIRCRAFT GUNS Filed May'23,.1941

11 Sheets-Sheet 2 Oct. 2, 1945. A. SVOBODA 2,385,952

FIRE DIRECTOR APPARATUS FOR ANTIAIRCRAFT GUNS Filed May 23, 1941 ll Sheets-Sheet 3 44 7im/vsfiafivvw Lil If. LIT?" 0 /fi5 MM 5% INVENTOR.

Oct. 2, 1945. SVOBODA 2,385,952

FIRE DIRECTOR APPARATUS FOR ANTIAIRCRAFT GUNS Filed May 23, 1941 ll Sheets-Sheet 4 [3% Mafia: r

ATTORNEYS Oct. 2, 15. A. SVOBODA 2,335,952.;

FIRE DIRECTOR APPARATUS FOR ANTIAIRCRAFT GUNS Filed May 25, 1941 ll Sheets-Sheet 5 D I a f/ INVENTOR uv'flv a ATTORNEYS Oct. 2, 1945. A. SVQBODA 2,385,952

FIRE DIRECTOR APPARATUS FOR ANTIAIRCRAFT GUNS Filed May- 25, 1941 11 Sheets-Sheetfi ATTORNEYS Oct. 2, 1945.

A A. SVOBODA FIRE DIRECTOR APPARATUS FOR ANTIAIRCRAFT GUNS Filed May 23, 1941 11 Sheeis-Sheet '1 INVENTOR.

B ZVMLJ'M r Oct. 2, 1945. SVQBODA FIRE DIRECTOR APPARATUS FOR ANTIAIRCRAFT GUNS Filed May 23, 1941 11 Sheets-Sheet 8 INVENTOR hm .Su-zrfi'MQ W A ORNEY A Oct. 2, 1945. A. SVOBODA 2,335,952

FIRE DIRECTOR APPARATUS FOR ANTIAIRCRAFT GUNS Filed May 25, 1941 11 Sheets-Sheet 9 A INVENTOR. m 5 w 40 42? /6 M 5/ Oct 1945 A. SVOBODA FIRE DIRECTOR APPARATUS FOR ANTI AIRCRAFT GUNS ll Sheets-Sheet 10 Filed May 23, 1941 Q BY W QQ Y a zMv/M, ATTORNEYS Get. 2, 1945. svo o 2,385fi52 FIRE DIRECTOR APPARATUS FOR ANTIAIRCRAFT GUNS Filed May 23, 1941 ll Sheets-Sheet ll mwavroa 8m in 4 g Wm r TTOF/ E'YS Patented Oct. 2, 1945 UNITE 2,885,952 FIRE DIRECTOR APPARATUS FOR I: GUNS Antonin svoboda, Forest Application May-23, 1941, Serial No. 394,954 In France May 23,1940

19 Claims.

This invention relates to a fire director apparatus for anti-aircraft guns. 1

The fire director apparatus which I have invented combines the use of polar and rectangular coordinates in such a way that, while the calculations and the indications to the operators of the apparatus are in rectangular coordinates, the connections between various parts of the apparatus move in accordance with corresponding polar coordinates. The apparatus thus combines the facility which is obtained by using rectangular coordinates for calculations and observations with the mechanical advantages and accuracy obtained by the use of rotary shafts.

The new fire director apparatus incorporates a number of new mechanisms which are necessary to its successful operation and which are also useful in other connections. These new mechanisms include:

(1) An apparatus for obtaining rotary movements which are functions of polar coordinates of a moving point whose rectangular coordinates are known, and also for obtaining rotary movements proportional to the differences between functions of the polar coordinates of two moving points when the differences between the rectangular coordinates of the moving points are given.

(2) Training and elevating mechanism for automatically varying the training and elevation angles of an instrument to keep the axis of the instrument directed at a point moving on a fixed course at a constant height at a constant speed.

(3) A computing device or predictor for indicating the value which a function of time will have after a variable time interval, and

(4) A computing device or predictor for indicating a close approximation to the value which a function of time will have after a fixed predetermined time interval.

As each of the four mechanisms is, so far as I am aware, entirely new in principle and in operation, it will be necessary to describe each of these mechanisms in order that the operation of the fire director apparatus in which they are included may be understood.

The drawings accompanying this specification are as follows:

(1) Apparatus for obtaining rotary movements which are functions of polar coordinates of a moving point whose rectangular coordinates are known Fig. 1 is a simplified perspective view showing the essential moving parts of the apparatus;

Figs. 2 and 3 are diagrams showing the derivation of the equations on which the apparatus is based;

form

Fig. 7 is the details showing the mounting of the disc Ill in Fig. 6;

Fig. 8 is a diagrammatic view of a changespeed transmission which may be substituted for the variable-speed transmissions shown in Fig. 6;

Fig. 9 is a diagrammatic view of a modified 'form of the apparatus for obtaining rotary movements proportional to the difierence between functions of two sets of polar coordinates;

Fig. 10 is a diagrammatic perspective view of a transformer which may be substituted for the transformer part of the apparatus shown in Fig. 9.

(2) Training and elevating apparatus Figs. 11 and 14 are diagrams for use in explaining the principle of the apparatus;

Fig. 12 is a diagrammatic perspective view of automatic training and elevating apparatus in which the constants of the targets movement are introduced manually;

Fig. 13 shows an indicating apparatus which may be used with the apparatus of Fig. 12 to insure accuracy in the manual introduction of the constants of the targets movement;

Fig. 15 is a modified training and elevating apparatus in which the constants of the targets movement are introduced automaticallyby mere- 1y pointing the telescope at the target for a few moments.

(3), (4) Predictors Fig. 16 is a diagrammatic plan view ofv a computing device for indicating the value which a function of time will have after a variable predetermined time interval;

Fig. 1! is a diagrammatic plan view of a predictor for indicating a close approximation to the value which a function of time will have after a fixed predetermined time interval.

(5) Fire director apparatus which are functions of the polar coordinates of a moving point whose rectangular coordinates are known responding to changes in the rectangular coordinates 01' the point,.butthe reverse of this is not true. The bearing angle of a point located near the origin of a system of polar coordinates changes so rapidly with sllght ichanges in the rectangular coordinates of the point that it is impracticable to provide an accurate mechanism in which elements moved in correspondence to changes in the rectangular coordinates eflect movements corresponding to changes in corresponding polar coordinates.

To overcome this diillculty, I supplement a transformer" mechanism for transforming polar coordinate movement of a pair of shafts into rec-' tangular coordinate movements of an observable element with a device, which I term a "distributor," in which two manually operated actuators are so interconnected with polar coordinate shafts that the turning of one of them moves the observable element so as to change only one rectangular coordinate, while the turning of the other actuator changes only the other rectangular coordinate. With this device, it is a simple matter to obtain rotary movements which are functions of the polar coordinates of a moving point when the value of rectan ular coordinates of the point are given. All that is necessary is to turn one actuator so as to make the required changes iin the value of one rectangular 00-,

ordinate of the observable element, and to turn the other actuator independently to make the required changes in the value of the other rectangular coordinate of that element. The interconnections between the two actuators and the two shafts of the distributor are based on a mathematical relation between changes in the polar coordinates of a moving point and the corresponding changes in the rectangular coordinates I of the point.

To adapt the apparatus for producing rotary movements proportional to the differences between the polar coordinates of two moving points, it is necessary only to make a slight modification in the distributor and to combine it with two transformers.

I will first explain the principle of my apparatus. As shown in Fig. 1, the apparatus consists essentially of the following moving parts: an element A movable in any direction in a plane XY, turnable' shafts B and C, and turnable actuators E and F. The plane in which the element A is movable contains two fixed perpendicular axes of reference OK and CY, and mechanical or visual means for measuring its distance from each of these axes and thus indicating the values of the rectangular coordinates of the position of the element A in its plane at any time. The actuators E and F may consist of cranks which may be turned manually. They are connected to the shafts B and C to turn the shafts, and the shafts are connected to the element A to displace the element A in its plane The element A and the connections between the shafts B and C and the element A constitute the part of the apparatus whch I term the transformer. These connections are such that tuming movements of the shaft B change the dis- (1) "Apparatus for obtaining rotary movements tance between the element A and the point 0 without changing its hearing from the point 0, while turning movements of the shaft C change the bearing of the element A from the point 0 without changing its distance from the point 0.

The actuators E and F, and the connections be. tween them and the shafts LB and C constitute the part of the apparatus which I term the distributor; These connections are such that tuming movements of the actuator E turn the shafts B andC in such manner as to move the element A parallel to the axis 0X, while turning movements of the actuator F turn the shafts B and C in such manner as to move the element A parallel to the axis OY.

To explain the nature of the connecting mechanism, it may be assumed that at some instant of time, the positions of the movable parts A, B, C, E and F are as follows:

The element A is at a distance u'irom the axis OK and at a distance a: from the axis OY and at a distance r from the point 0, and the bearing angle of A from 0 measured from the axis ox is o.

The shaft B has turned through an angle b and the shaft C has turned through an angle 0.

The actuator handle E has turned through an angle e and the handle of the actuator F has turned through an angle 1.

In a time interval dt, the actuator E is turned through an arc de, and the actuator F is independently turned through an are d and this results in turning the shaft B through an arc db, and the shaft C through an arc dc, moving the element A so as to change its polar coordinates by increments dr and dg and its rectangular coordinates by increment da: and dy.

The connections between the parts are such that r is a function of b and is independent of 0,

while a is a function of c and is independent of b, while at the same time :1: changes with e and is independent of f, and 1! changes with f and is independent of e.

The relations between dr, do, da: and dy may be determined geometrically from the diagrams Figs. 2 and 3 as follows:

angles AMA and ANA. The lengths of the sides of these triangles are indicated in Fig. 3. The side AN'represents an arc of radius r swung through the infinitesimal angle do and is, therefore, rda. The lengths of the other sides are the infinitesimal increments of the coordinates r, x and 11.

Since the broken line AMA'NA forms a closed figure, the length of an orthogonal projection of this line on any straight line must be zero. By projecting the parts of this broken line on the straight line ON, we obtain 'AM cos g+MA' sin g+A'N cos -NA cos 0=0 Inserting the values of the lengths of the parts of the broken line,

dz cos o+dy sin g+0-dr=0 Transposing, we obtaindr=dm cos g+dy sin 9 (l) Projecting the parts of the broken line AMA'ANA on the straight line NA, We obtain MA cos g-AM sin g-A'N cos +NA cos 90=0 Substituting the values oi the len hs of the parts of the broken line,

d1 cos a-da: sin grdu+0=0 Transposing and dividing by r, we obtain l m 2 (2) Solving Equations 1 and 2 for do: and till, we obtain da:=dr cos g-rdg sin 0 (3) and dy=dr sin c+rdc cos a (4) Now, if the connections between the shafts B and C and the element A are made such that radial movements of the element A are proportional or (to simplify) equal to turning movements of the shaft B while angular movements of the element A are equal to turning movements of the shaft C or, in other words so that b=r and hand c, may be substituted for r and gin Equations 1 and 2:

db=da: cos 0 +111! sin c (5) do: da: sbin c dy (20s 0 (6) Equations 5 and 6 will then give the relation between turning movements of the shafts B and C and the changes thereby caused in therectangular coordinates x, y of the element A, Now if the mechanical connections between the actuators E, F, and the shafts B, C, are such that turning movements of the shafts B and C are related to the turning movements of the actuators E and F by the following equations:

db=de cos c+df sin c (7) de: d e sb n c df cbos c (8) it is evident from comparison of Equations 5 and 6 with Equations 7 and 8 that:

dx=de and so that with such mechanical connections tuming movements of the actuator E will move the element A through the shafts B and C so as to change the a: coordinate of the-element A by an amount equal to turning movement of the actuator E, while at the same time the turning movements of the actuator F will be reproduced as changes in the ycoordinate of the element A.

The apparatus which has been described is illustrated diagrammatically in Fig. 4. The distributor part of the apparatus is shown schematically by arrows which represent mechanical connections, such as shafts, for transferring mechanical movements, and boxes which represent devices for combining the mechanical movements which are brought to them by multiplication, division, addition or subtraction as indicated by the symbol on each box. Thus, the boxes marked 0: and may contain variable-speed transmissions, while the boxes marked and may contain diflerentials. The boxes marked "sin, "cos represent mechanical devices for translating a movement proportional to the angle into a movement proportional to the indicated trigonometric functions of the angle. In the distributor, the connections between the cranks E and F and the shafts B and C operate in accordancewith Equations 7 and 8, and in the transformer the clmnges in the polar coordinates of the element A are equal or proportional to the turning movements of the shafts B and C respectively, so that turning the actuators E moves the slide Ax measuring the a: coordinate of the element A without moving the slide Ay and measuring the 1! ordinate of the element A, while turning the crank F moves the slide Ar without moving the slide Ax.

My invention is by no means limited to the use of connections such as are indicated in Fig. 4, for it is not essential that the changes in the rectangular coordinates of element A be equal to the turning movements of the actuators E and F, but merely that the change in the a: coordinate be caused only by the turning movement of the actuator E and the change in the y coordinate be caused only by the turning movement of the acator F. Furthermore, it is not essential that the turning movements of the shafts B and C be equal to the changes in the polar coordinates r and 9 but merely that the change in the coordinate r be a function of the turning movement of the shaft B and the change in the coordinate a be an independent function of the turning movement of the shaft C. The connections between the elements of my apparatus, therefore. need not be those specifically indicated in Fig. 4. The required connections are as follows:

Connection B-A must be such that b=j(r) i. e. db=df(r) (9) Connection C-A must be such that c=F(g) i. e. dc=dF(g) (10) Since, as appears from Fla. 2,

m=r cos y (11) and y=r sin y While any such connections may be used within the scope of my invention, an important speciflc feature of my invention consists in selecting functions which lead to simple and accurate mechanical connections. In accordance with this feature of my invention, I select the functions indicatedin the above equations as follows:

b=j(r) log,1-, (so that (a (9a) c=F(g) Eg (so that dc=d9 on (b, 0) secs c=c0s 9; \Pl (b, c) Esin c=siri 9 c2 (12, c) 5008 c=c0s 9; il (b, c) E-S1Ii c=-sln g tfi 13 and 14 then become d:c=r.db.cos g-r.dc.sin y (17) dy=r.db sin 'g+r.dc.cos 9 (l8) Substituting in Equatioml'? the values of db and dc given by Equations 13a and 140, we obtain r.(sin g.de+cos g.df). sin g which simplifies to d:1:=r.de (20) In the same way the substitution in Equation 18 of the values of db and dc given by Equations 13a and 14a gives di l=1.df (21) Since the values of 11:1: and dy given by Equations 20 and 21 have the form required by Equations 15 and 16, it is demonstrated that the functions selected comply with the requirements specifled in the general case. The connections between B and A and between C and A specified by Equations 9a and 10a and the connections between E, F, B and C specified by Equations 13a and 14a thus constitute ,a specific example of the connections specified more generally by Equations 10 to 16 inclusive.

' The form of my invention which I consider best is based on the connections specified by Equations 9a, 10a, 13a and 14a and is indicated schematically in Fig. 5. The symbols used on Fig. have the same significance as on Fig. 4. The dotted arrows on Fig. 5 may be either rotary shaft connections or sliding frame connections.

A mechanism for carrying out the operation shown schematically in Fig. 5 is shown in the perspective view, Fig. 6.

In the distributor part of the apparatus shown in Fig. 6, the actuators E, F are shown as cranks arranged to rotate friction discs I0, I l, which are rotatably mounted as shown in Fig. 7. These two discs are in the same plane. Across the faces of the two discs above and below the discs extend four shafts, |2, |3, l4, l5, each of which is parallel to a line connecting the centers of the discs. On the shafts are splined friction rollers l6,. l1, -l8, I9 whose peripheries ride on the upper and lower faces of thediscs Ill, The shafts |4 and|5 are connected to the shaft B by a differential 20 arranged to make the turning movement of the shaft B equal to the sum of the turning movements of the shafts l4 and IS. The shafts I2 and II are connected to the shaft C. through a differential 2| arranged to make turning movements of the shaft C equal to the difference between the turning movement of the shafts l3 and turning movement of the shaft l2. -The longitudinal positions of the discs l6 and IS on their'shafts |2 and I5 is controlled by a sliding frame 22 having a slotted bar 23 engaging a crank 24 on a shaft 25. The longitudinal positions of the discs I] and I8 on their shafts l3 and I4 is determined by a sliding frame 26 having a slotted bar 21 engaging a crank 28 set at 90 from the crank 24 on the shaft 25. The

shaft 25 is connected by gears and a shaft W to the shaft C, so that its turning movements are equal to those of the shaft C.

In the transformer part of the apparatus shown in Fig. 6, the element A has the form .of a rod mounted on a slide 40 on an arm 4| fixed to the shaft C. The lower end of the .rod A engages a slot 43 in a disc 42 carried by a hollow shaft. The slot 43 has the form of an equiangular or logarithmic spiral. The rectangular coordinates of the rod A, referred to perpendicular axes parallel to the disc 42 and intersecting on the axis of this disc and the shaft 0, are indicated b slides A1, A1! such as shown in Fig. 4 engaging the rod A.

The transformer part of the apparatus incor- A porates the connections specified in Equations 9a and 10a. The connections between the shafts B and C and the rod A are such that the shaft B controls the distance between the axis of the disc 42 and the rod A, while the shaft C controls the bearing angle of the rod A from this axis. The arm 4| is driven directly from the shaft C. The disc 42 and hollow shaft 44 are driven by a gear 46 on a shaft 41 extending from a differential 4| which adds together the turning movements of the shaft B and the shaft C. Thus, the turning of the arm 4| is proportional to the turning of the shaft C, while the turning of the disc 42 relative to the arm 4| is proportional to the turning of the shaft B, so that movements of the rod A around the axis of the disc are equal to turning of the shaft C, as required by Equation 10a, while radial movements of the rod A caused by the engagement of the rod with the slot 43 are caused by turning movements of the shaft B and are an anti-logarithmic or exponential function of such turning movements, as required by Equadiscs lo and II is equal to the sine of the angle g proportional to de sin 9 because, as has been said,

the distance of this roller from the center of the friction disc I0 is equalto sin y. The roller l8 and the shaft l4 are turned through an angle proportional to de cos g. If at the same time the actuator F is independently moved through a small angle df, the disc I turns the roller l1 and the shaft l3 through an angl proportional to (if cos y and turns the roller l9 and the shaft l5 through an angle proportional to di sin y, the turning movement of the shaft l4, proportional to de cos g, and the turning movement of the shaft l9, proportional to df sin 9, are added in the differential 20 so that the turning movement of the shaft B is proportional to de cos g+df sin y as required by Equation 13a above. The tumin'g movement of the shaft l2, proportional to de sin y, is subtracted from the turnin movement of the shaft [3, proportional to df cos min the differential 2|, so that the turning movement of the shaft C is proportional to de sin g+df cos g as required by Equation 14a.

Any turning movement given to either actuator, of course, changes the angle 9 and, therefore, the values of the sine and cosine of this angle; but the connection of the shaft 25, with the shaft C through the shaft W automatically adjusts the positions of the rollers l6, l1, l8, E9 on their shafts so that the distance of the rollers l5 and i9 from the centers of the discs 80 and H is maintained equal to sin while the distance of the other two rollers IS, H from the centers of the friction discs is maintained equal to cos The distributor part of the apparatus, therefore, continuously makes the calculations called for by Equations 13a, 140.

Since the transformer part of the apparatus operates in accordance with Equations 90, 10a, and the distributor part in accordance with Equations 13a, 14a, any movement of the handle or actuator E moves the rod A parallel to the X axis, while any movement of the actuator F moves the rod A parallel to the Y axis.

In the use of the apparatus, the actuators E and F are manipulated by operators observing the element A. The operator of the actuator E observes movement of the slide A2: and makes such turning movements as are necessary to keep the :r-ordinate of the rod indicated by the position of this slide A always equal to given values of the x-ordinate of some object to be followed, while the operator of the actuator F watches the slide A11 and makes such turning movements as are necessary to keep the y-ordinate of the rod A always equal to given values of the y-ordinate of the object. This can be done without any interference, as the movements made by the operator of the actuator E in no way affect the y-ordinate which the operator of the actuator F is controlling, and in the same way movements of the actuator F in no way aifect the :c-ordinate. So far as the operators of the actuators E and F can see each is merely adjusting a. slide indicating one of the rectangular coordinates of the element A; but in doing this by means of this apparatus .the two operators cause rotations of the shafts B and C which are functions of the polar coordinates corresponding to the rectangular coordinates which they are adjusting. The shafts B and C may, therefore, be connected so as to operate any apparatus, such as a telescope, or a gun whose position is normally determined by a pair of polar coordinates.

In Fig. 8 is shown a modification of a part of the apparatus shown in Fig. 6. The purpose of the modification is to avoid the use of the friction discs shown in Fig. 6. It will be noted that in Fig. 6 the actuator E is connected to the shafts l2 and it through variable-speed transmissions constituted by the disc Ill and rollers l6 and I8, while the actuator F is connected to the shafts l3 and I5 through variable-speed transmissions constituted by the disc II and the rollers l1 and I9. I have found that it is possible to substitute positive change-speed transmissions consisting of gear wheels for these frictional transmissions and that it is desirable to do so where the device is used with heavy load which might cause slip- The apparatus shOWn in Fig. 8 may be substituted for the frictional variable-speed transmission between the actuator F and theshaft l3 which in Fig. 6 is formed of disc H and the roller If, and for the means for'controlling this var1- able-speed transmission, which in Fig. 6 is constituted by the crank 28, the bar 21 and the slide 25. In one complete revolution of the crank 28, which corresponds to a change of 360 in the angle 9 (owing to the connection .between the shaft 25 and the shaft C through the shaft W as heretofore explained), the roller i1 is moved back and forth across the face of the disc ll so I that the gear ratio of the transmission H-I'| varies continuously from +1 to 1 and back to +1 in accordance with changes in the cosine of the angle 9. While a transmission providing for continuous change of speed in both directions is necessary to make the operation of the apparatus theoretically correct, I have found that an approximation which is satisfactory in practice can be obtained by using a transmission providing for three speed ratios in one direction which correspond to the speed ratios of the frictional transmission when the disc I? is at three different points at one side of the axis of the disc H, and three speed ratios in the opposite direction which correspond to three positions of the disc l! at the left side of the axis of the disc H and providing also a neutral position which corresponds to placing the disc H on the axis of the disc ll. Such a transmission is shown in Fig. 8.

In Fig. 8 the crank F is connected by means of bevel gears 51 to two concentric shafts B8, 49, which it thus causes to rotate in opposite directions. A set-of change-speed gears connect the shafts 48 and 49 with the shaft 13'. The shaft 58 carries a group of three gears 50, 5|, 52, of decreasing diameter. The shaft 59 carries the same number of gears 53, 55, 55, of increasing diameter. A shaft 56 is slidably connected to the shaft l3 and is urged toward the left by means of a spring 51. Upon this shaft there are keyed two groups of three gears 58, 59, 60 and 6!, 62, 63. The diameter increases from the gear 58 to the gear 60, which is equal to the gear GI, and then the diameter decreases down to the gear 63. The distances between the various gears that are carried by the parallel shafts 48, 49 and 56, are such that only one of the gears of the shaft 56 can come into engagement with a gear of the shaft 48 or of the-shaft 49. In the central position, there is a free point in which none of the gears engage. By shifting the shaft 56 lengthwise, the pair of gears adapted for obtaining a desired gear ratio may be engaged.

The speed ratio of the gear transmission is controlled electromagnetically by a switch arm 16 fixed on'a shaft 25' which corresponds to the shaft 25 of Fig. 6 and which, like the shaft 25 is driven by the shaft W so that its turning movements are equal to changes in the angle g. The electromagnetic means by which this switch arm controls the gear ratio of the transmission, in the specific form shown in Fig. 8, are as follows:

' A tubular casing 64, located on the extension of the shaft 56, encloses two electromagnets 65, 66 which are fixed to this-casing. A'third electromagnet 61 is aligned with the preceding ones. It is held stationary in a casing 68. The electromagnet 65 has only one winding. The two electromagnets 66 and!" are each provided with two concentric windings. The effects of these windings annul each other. The movable core 'of the electromagnet 65 is integral with the shaft 56. The movable core of the electromagnet 66 is integral with that of the electromagnet 61. The stroke of the plunger core of the electromagnet 66 is three units. that of the core of the electromagnet 66 is two units, and that of the core of the electromagnet 61 is one unit. The winding of the electromagnet 66 is connected in series.

with the inner winding of the electromagnet 66. The outer winding of the latter is connected in series with the inner winding of the electromagnet 61. One end of the two inner windings 68 and 61 and one end of the outer winding 61 are connected to one of the poles of a source of current 69. The winding of 65, and outer winding of 66 and the outer winding of 61, are connected to a series of contact plates, to 16, which are in the form of segments of concentric circles and which partially overlap. These contact plates are traversed by the switch arm 16, the axis of which is connected to the second pole of the source of current. The respective length of each of these segments and their distribution about the axis of rotation of the arm 16 are such that the passage of the arm 16 over them corresponds to various combinations in the excitation of the electromagnets 65, 66, 61. For each of these combinations, the shaft 66 is displaced lengthwise against the force of the spring 51. In a half rotation of the arm 16, the shaft is placed successively in seven different positions which correspond to the engagement of different pairs of gears and to the central free point. When the arm 16 turns through an angle a and the crank F is turned through a small angle d), the shaft 56 and the shaft H are turned proportionally to d! cos y with an approximation which is satisfactory in the practical use of the of Fig. 6, a precisely similar device is used to replace the transmission 'llll8 of Fig. 6, while the transmissions Ill-l6 and H-|9 of Fig. 6 are replaced by transmissions precisely like that shown in Fig. 8 except that the controlling arm corresponding to the arm 16 of Fig. 8 is mounted on the shaft 25 at 90 from the position of the arm 16.

By a simple modification, the apparatus which has thus far been described may be adapted for obtaining rotary movements which are proportional to the differences between functions of the polar coordinates of two moving points when the differences between the rectangular coordinates of the two moving points are given. In Fig. 9, I have shown the adaptation of my apparatus to this use.

The apparatus shown in Fig. 9 contains two transformers which are substantially similar to the transformer part of the apparatus shown in Fig. 6. The two movable elements A1, As shown in Fig. 9 may consist of rods like the rod 1A of Fig. 6, projecting towards each other so that their opposed ends are in substantially the same transverse plane. The element A1 engages slots in two perpendicular slides 82, 83 and the rod A: engages slots in. similar slides 86, 81. The distance between the slides 82 and 88, Arc, is the difference between the :c ordinates of the elements A1 and A2, while the distance between the slides 83 and 81, A11, is the difference between their 11 ordinates. Two shafts B1, C1 are connected to the element A1 in such manner that turning of the shaft B1 determines the distance of the element -A1 from a fixed point 0, while turning of the shaft C1 de termines the bearing angle in of the element A1 to the point 0. Two shafts B2, C2 are connected to the element A: in precisely the same manner. The

two sets of connections are shown as similar to the connections between the shafts B and C and the element A in Fig. 6 except that a disc 1, 6|: with a radial slot is substituted for the arm ll of Fig. 6 but, in the broadest aspect of the invention, it is necessary merely that the turning movements of the shafts be functions of the polar coordinates of the movable elements as follows:

A pair of driving shafts B3, C3 are connected directly to the shafts B2, C2, and are connected to the shafts B1, C1 through differentials 88, 88. Another pair of shafts B4, C4 enter the differentials 88, 88, and the differentials are so arranged as to make the turning of the shaft B1 equal to the sum of the turning of the shafts B3, B4, and the turning movement of the shaft C1 equals the sum of the turning of the shafts C3, C4.

Shafts B4. C4 are the output shafts of a distributor which may be precisely like the distributor part of the apparatus shown in Fig. 6, except for a difference in the connection of the return shaft W hereafter explained. The shafts B4, C4 are turned by cranks or actuators E, F which are interconnected with the shafts B4, C1 through variable-speed transmissions in the manner indicated in Fig. 5 and. illustrated in Fig. 6. The control for the variable-speed transmissions of the connecting mechanism is, however, not connected to the shafts B4, C4 which correspond to the shafts l3 and C of Fi 6, but is connected instead to the shaft C1, through shaft W1. This is necessary because it is the shafts B1, C1, not the shafts B4, C4, which are connected to the element A1, and whose turning movements are, therefore, functions of the polar coordinates of the element A1 required for controlling the variable-speed transmissions of the connecting mechanism between the actuators E. F and the shafts B4, C4. The shaft W1 controls the variable-speed transmissions in the same way as the shaft W of Fig. 6.

It is not essential to use the distributor connections indicated in Figs. 5 and 6 as any type of connections within the scope of the general Equations 13-16 may be used provided that both the transformers produce movements corresponding to Equations 9 and 10.

In the initial setting of the apparatus shown in Fig. 9, the elements A1 and A: may be set in coincidence so that the slides 82 and 86 are coincident and the slides 83 and 81 are coincident. So long as the actuators E and F are stationary, the shafts B1 and B: turn together, as do also the shafts C1 and C1, and the elements A1 and A2, therefore, remain coincident.

In the use of the apparatus, an operator stationed at the actuator E observes the slides 82 and 86 and turns the crank E until the slide 82 is separated from the slide 86 by the predetermined distance Act. He then continues to make such turning movements of the actuator E as he observes to be necessary in order to maintain the slide 82 constantly at this distance As: from the slide 86. At the same time, a second operator observes the slides 83, 81 and makes such turning movements of the crank F as he observes to be necessary to maintain the slide 88 at the distance A from the slide 81. These operations may easily be carried out since, as before explained, turning the crank E does not affect the position of the slide 83, while turning of the crank F does not ailect the position of the slide 82.

As a result of the turning movements of the cranks E and F, necessary to maintain the slides 82 and 83 at the distances Aa: and Ag from the slides 86 and 81, the turning movements given to the shafts B4 and C4 are as follows:

that is to say, they are the difl'erences between functions of the polar coordinates of two moving points whose rectangular coordinates differ by the given values Am, A11.

While the modification which has been described is capable of many uses, one valuable use of it is to change the training and elevation of a gun directed at a target in order to direct it at the point where the target will be after the time of travel of the shell, when the diiference between the rectangular coordinates of the place where the target is and the place where the target will be after the time of the travel of the shell are known. When used for this purpose, it is sometimes desirable to have the operators of the cranks E and F observe some mechanically determined function of A1: and Ag rather than observe the values of A11: and Ag directly. When this is the case, it is desirable to use a modification of the transformer part of the apparatus shown in Fig, 9. This modification is shown in Fi 10.

The double transformer shown in Fig. 10 is similar to that shown in Fig. 9 except that a single rod Axis substituted for the two rods A1, A2, and the discs M1 and $21 which position the rod A1 in Fig. 9 are mounted on a movable shaft 90 instead of being mounted on a fixed pivot as they were in Fig. 9. The shaft 90 is mounted in a block 9| which engages and is carried by two slides 92, 93. The slides are mounted on a fixed square frame 94 so that the movement of one slide is at right angles to that of the other. The center of the square frame 94 is on the fixed axis of the discs Q is, 522. Because of the movable mounting of the discs M1 and 421, the shafts C1 and B1 are connected to the discs through flexible shafts held at one end On the block 9|. One of these flexible shafts 95 is shown in Fig. with its end held in an arm 98 of the block 9 I.

It will be understood that in the diagrams Fig. 9 and Fig. 10, the four discs are widely separated for the sake of clearness, while, in the actual apparatus, they are, of course, placed close together, and, in the apparatus shown in Fig. 10, close to the frame 96.

The operation of the modified transformer arrangement shown in Fig. 10 is precisely like that of the double transformer shown in Fig. 9, except for such difference as arises from the fact that a single rod A3 replaces the two rods A1, A2 of Fig. 9 and the shaft 90 of the discs M1 and 421 is movable. The rod A3 of Fig. 10 is positioned by the discs M2, 522 in the same way that the rod As was positioned by these discs in Fig. 9. If the discs M1 and 521 were stationary, the movement of the rod A: by the discs M2, 322 would result in a corresponding movement of the movable shaft 9|! and the block 9!; but when the discs M1 and $21 are turned, the reaction between them and the rod A3 causes a movement of the shaft 90 and block 9! which is the reverse of the movement which is given to the rod A1 by the discs M1 and 521 of Fig. 9. Consequently, the horizontal distance from the slide 92 to the vertical center line of the fixed frame 94 is' maintained equal to At, while the vertical distance from the slide 93 to the horizontal center line of the frame 96 is maintained equal to Ay. oz: and A2! are thus measured from fixed points, instead of from movable points as in Fig. 9. This is a decided advantage when it is desired to have the operators of the cranks E, F of the distributor observe functions of Am and Ag], since apparatus for computing these functions may be directly connected to the slides 92 and 93.

The apparatus illustrated in Fig. 9 may be used for obtaining rotary movements which are functions of the polar coordinates of a moving point when the approximate values of these functions are given and exact values of the rectangular coordinates of the point are given. When the apparatus is used for this purpose, the element A2 and the shafts B2 and C2 may be omitted. The driving shafts Ba and C3 are rotated proportionately to the given approximate values of functions of the polar coordinates of the moving point. The actuator E is manipulated to make the observed :c-ordinate of the element A1 equal to the exact given value of the arr-ordinate of the moving point, and at the same time the actuator F is manipulated to make the observed y-ordinate of the element A1 equal to the given exact value of the y-ordinate of the moving point. The result of this manipulation is that the shafts B1, C1 are turned in proportion to functions of the exact values of the polar coordinates of the moving point.

The turning of the shafts B1 and C1 thus obtained are the same as the turning of the shafts B and C obtained by the apparatus of Figs. 5, 6 and this result is secured with very much less turning of the actuators E and F than is required in the apparatus of Figs. 5 and 6, since the major part of the turning movements of the shafts B1 and C1 come from the driving shafts B3, C3.

(2) Training and elevating apparatus This apparatus provides automatic means for varying the trailing and elevation angles of an instrument to keep the axis of the instrument directed at a point moving on a fixed course at a constant height at a constant speed.

The apparatus includes training and elevating shafts connected to a telescope or other instrument, constant speed motors connected to these shafts through variable-speed transmissions, and controls for the transmissions which, when set in accordance with the constants of the target's movement (course angle, height and speed), control the transmissions so as to keep the telescope directed at the target. The use of complicated calculating mechanism in the controls of the variable-speed transmissions is avoided by connecting the elevating shaft to the telescope in such manner that any turning movement of this shaft is proportional to the logarithm of the cotangent of the angle by which this turning movement changes the elevation of the telescope.

.I will first explain the principle of the invention. Fig. 11 shows the course HG of an airplane which is assumed to be flying along this course at a constant speed c and a constant height h. KJ is a projection of the course HG on a horizontal plane containing the point 0 at which a telescope is located. 00' is a fixed vertical plane of reference from which bearing angles are measured. The course HG makes an angle a wtih the plane to. The constants of the airplane movement are, therefore, the course angle a, the height h and the speed c.

The changes which must be made in the training or bearing angle a and the elevation angle s of the telescope located at II in order that the telescope may follow the airplane depend upon the constants a, h and 0, but the rate of change or time derivative of the elevation angle s does not bear a simple-relation to these constants.

I have discovered that the time derivative of the logarithm of the cotangent of the angle of elevation bears a relation to the three constants of the target movement which is simple and analogous to the relation of the time derivative of the bearing-angle to these constants. I will first point out what these relations are and then show how I have utilized them to provide a simple mechanical apparatus for maintaining the telescope pointed at the airplane.

It appears from Fig. 11, which indicates movement of the airplane from G to G and of its projection from J to J in a small time element (it, that cdt sin (cl-g) =h cot sdg (22) cdt cos (a-g) =d(h cot s) :M cot s (23) which by differentiation is equal to 1 92 cots dt may be derived as follows:

d log cot s cos (ag) dt h cot s It will be noted that Equations 24 and, 25 Show that the two time derivatives selected bear simple and analogous relations to the three constants I a, c and h. The values of the two time derivatives differ only in that one of them involves the sine of the angle (a-g), while the other involves the cosine of the same angle. The values given by the two equations are, therefore, the rectangular coordinates of a point whose polar coordinates are:

My apparatus is based on Equations 24 and 25.

Fig. 12 shows an embodiment of my training and elevating apparatus in which the constants a, h and c of the target's movements are introduced manually. Training and elevating shafts are connected to a telescope I00 in such manner that the training or bearing angle 9 of the telescope is proportional to turning movements of the shaft III), while the elevating angle s of the telescope is proportional to the anti-cotangent of the anti-logarithm of turning movements of the shaft III. The shafts III] and III are turned by the constant speed motor (not shown) which drives two friction discs H2, H3 at constant speeds. In the drives are incorporated variablespeed transmissions II4, III. A control 6 for the variable-speed transmissions is set in accordance with the constants of the targets movement. and, when so set, regulates the transmissions to drive the training shaft IIII at the speed given in Equation 24 and the elevating shaft I I I at the speed given in Equation 25.

The connection between the training shaft II 0 and the telescope is as follows: A gear I26 on the shaft III engages a gear I2I fixed on a hollow shaft I22. At the upper end of the hollow shaft I22 is a gear I23 meshing with a gear I24 of a shaft I25 journalled on a pivoted frame I26 of the telescope I". Shaft I25 carries a pinion I21 meshing with a fixed circular gear rack I26. The training of the telescope is, therefore, proportional to the turning of the training shaft Ill, and, for simplicity, it will be assumed that the gear ratios are such that any angular turning of the shaft I I6 turns the telescope frame through the same angle as that through which the shaft I I0 is turned.

The connection between the elevating shaft III and the telescope IN is as follows: A crank I36 on the rocking arm- I3I of the telescope I46 enga es a spiral groove I32 in a disc I33 mounted on the-pivoted frame of the'telescope. The disc I33 is driven through a gear I34 which is fixed on a shaft I36 which passes through the hollow shaft I22. The shaft I36 is driven from a differential III which adds the turning movements of the shafts III! and III so that the turning of'the. shaft I36 relative to the hollow shaft I22 and the pivoted frame of the telescope is equal to the turning of the elevating shaft III. The connection described is such that, when the elevating shaft III is turned to elevate the telescope through an angle s, the turning movement of the shaft III which causes this elevation is proportional or equal to log cot s.

The connections between the variable-speed transmissions H4 and H5 and the training and elevating shafts III and I II include means for supplementing the mechanical turning of these shafts by manual turning. The output shaft I46 of the transmission H4 is geared to shaft I, and a shaft I42 which may be turned by a hand wheel I43 entersa differential I44 which adds the movements of the shafts I and I42 and transmits'the sum to the training shaft IIII through a shaft I46 and gears I46. The output shaft I" of the transmission H5 and a hand wheel I46 are similarly connected to the elevating shaft II I through a differential I46. The shafts HI and I41 may contain clutches Ia and Mia to permit disconnecting of the mechanical drive so that the training and elevating shafts may be turned directly by the hand wheels I43 and I46 in the initial setting of the telescope.

'The variable-speed transmissions II4, III are shown diagrammatically as consisting of friction wheels I50, I5l movable diametrically across the constant-speed, motor-driven friction discs H2, H3. The wheels I50, Iil are mounted on sliding hollow shafts I52, I63 keyed to the output shafts I40, I41 of the transmissions.

The controlling mechanism IIG for the variable-speed transmission is connected to the training and elevating shafts H0 and III and also with three hand wheels I54, I55, I56 which are turned to set the controlling mechanism in accordance with the constants of the target's movement.

The hand wheel I56 is turned until the constant course angle a of thetarget appears under a fixed pointer I51 on the dial I58 geared to the shaft I59 on which the hand wheel is mounted. The shaft I59 which is thus turned proportionately to the course angle a and a shaft I60 connected to the training shaft IIO by gears I6I enter a differential I62 which subtracts the turning of the shaft I60 from the turning of the shaft I59. Consequently, the output shaft I63 of this differential is turned proportionately to the difference between the bearing angle of the telescope and the course angle of the target, that is to say, in proportion to a-g.

The hand wheel I56 is turned until the constant height n of the target appears over the fixed pointer I60 on a dial I65 geared to the shaft I66 on which the hand wheel I56 is mounted. The dial I65 contains a logarithmic scale so that in setting the dial at h the hand wheel I56 and shaft I66 are given a turning movement proportional to log n. Another dial I61 is also geared to the shaft I66 so that the turning movements of this dial are equal to log h.

The hand wheel I58 is turned until a pointer I68 geared to a shaft I69 which is turned by the shaft I10 on which the hand wheel I54 is mounted indicates on the dial I61 the constant speed c of the target. The dial I61 is logarithmically graduated so that the setting of the pointer I68 by the hand wheel I54 after the hand wheel I56 has been set results in turning the shafts I10 and I69 through an angle proportional to log c-log h which is, of course, equal to log%.

The shaft I69 which is thus turned proportionately to log log %log cot s which equals 1 c 1 (E' Ts The shaft I63 and the shaft I14 are connected to a transformer I80 which transforms polar coordinate movements into rectangular coordinate movements like the transformers shown in Fi 9. The transformer I80 consists of two coaxial rotatable slotted discs I8I, I82 and a pin A engaging the slot in each disc.

The disc I8I is turned by the shaft I63 through gearing I84, a shaft I85 and a worm I86, and the gear ratios are so chosen that turning movements of this disc are equal to (a-g). The disc I8I contains a radial slot I81 which positions the pin A so that its bearing angle from a fixed reference line through the axis of the discs is equal to (ay).

The disc I82 is driven by a worm on the output shaft I89 of a difierential I98 which adds the movements of the shafts I63 and I14, so that the turning of the disc I82 with respect to the disc IN is proportional to the turning of the shaft I18 proportional to e 1 (Foot s) The disc I82 contains a slot I8I in the form of an equiangular spiral so that the turning of this disc in relation to the disc I8I positions the rod A at a distance from the axis of the discs proportional to I h cot s The pin A engages two slotted slides I92, I98 which slide at right angles to each other. The

. distance of the slot in the slide I02 from the center of the discs I8I, I82 is, therefore, equal to one rectangular coordinate, while the distance from the slot in the slide I93 to the center of the discs is equal to the other rectangular coordinate of the rod A whose position is determined by the two polar coordinates (11-57) and h cot s and, therefore, represent the values specified by the Equations 24 and 25. The slide I92 is connected to the transmission 4 in such a way as to position the friction wheel I50 at a distance from the axis of the friction disc II2 equal to the distance from the slot in this slide to the axis of the discs I8I, I82, and the slide I93 is similarly connected to the transmission II5. It follows that the speeds at which the two transmissions drive "the training shaft H0 and elevating shaft III are the speeds given by the Equations 24 and 25.

In using the apparatus of Fig. 12, the telescope I00 is first directed at an airplane by turning the hand wheels I83 and I88 with the clutches Mia and I810 disconnected. The clutches are then closed and the controlling apparatus 6 are set in accordance with the constants of the airplanes movement by (1) turning the hand wheel I55 until the dial I58 is set to the value 3 (course angle), (2) turning the hand wheel I56 until the dial I65 is set to the value h- (height of airplane), and (3) then turning the hand wheel I 58 until the pointer I68 is set on the disc I61 to the value of 0 (speed of airplane). During the setting operation, the hand wheels I43 and I 48 are turned sufliciently to keep the telescope pointed at the airplane, but, as soon as the setting has been made, the telescope will automatically follow the airplane without any further turning of any of the hand wheels so long as the course angle, height and speed of the airplane remain constant.

In order to use the apparatus in the manner described, it is, of course, necessary that the three constants of the airplanes movement be known shortly after the airplane is first seen. As a rule, they are known only approximately at this time so that the first setting of the hand wheels I55, I56 and I54 is only approximate. In this case, some slight turning of the hand wheels I43 and I88 is necessary to follow the airplane in the telescope. This continues to be the case until the constants of the airplanes movement have been determined accurately. The hand wheels I55, I56 and I58 are then reset more adcurately so that further turning of the hand wheels I83 and I88 becomes unnecessary.

In Fig. 13, I have shown an auxiliary apparatus which may be used with the training and ele- 

